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Wednesday, November 21, 2007

Blaise Pascal, Florin Périer, and the Puy de Dôme experiment

November days can be depressing, when thick fog is hanging in town for days and there is no real daylight. Here in Frankfurt, one can at least try to escape, and with some luck, the top of the Feldberg is above the mist, and in the sun. November 1647 in Paris may have been similar gloomy, and made Blaise Pascal daydream of the mountain peaks around Clermont-Ferrand, a town in provincial Auvergne where he had been born in 1623 and grown up, and where his sister and her husband Florin Périer still were living.

What is known for sure, however, is that in that fall, Pascal had the idea for an experiment that, simple as it may be, nevertheless revolutionised our knowledge about the atmosphere and atmospheric pressure. So, on November 15, he sat down and wrote a long letter to his brother-in-law to persuade him to conduct this experiment. It was nothing for an armchair scientist, however, since it involved ascending the more than 1000 meters to the top of the Puy de Dôme, the highest mountain in the vicinity of Clermont-Ferrand.

A few years before, engineers in Italy had begun seriously to wonder why they could not succeed in building suction pumps that would be able lift water for the usage in fountains or for the supply of buildings to a height of more than about 10 metres. They even had asked Galileo about this, but he could merely confirm the fact, and not provide a clear answer. In Rome, an amateur scientist named Gasparo Berti set up a series of experiments to study this curious phenomenon in detail. He used a long tube, sealed at one end, filled it completely with water, immersed the open end in a tub also filled with water, and then brought the tube in a vertical position. As he noted, some of the water poured in the tub, but not all, leaving a vertical column of water with a height of about 10 metres in the pipe - this was, obviously, exactly the limiting height of the pumps that had puzzled the engineers.

At the time, in the early 1640s, these experiments stirred quite an excitement. The big question was, is the space at the top of the pipe really empty? And what inhibits the water to pour out completely into the tub? According to the still prevailing physical theories going back to Aristotle, nature abhors the vacuum - there cannot be an empty space, thus, the space above the water line in the pipe has to be filled with some substance (not quite wrong, as we know today, since this space is filled with water vapour with the small vapour pressure at room temperature, but this was mostly not thought of to be the explanation). And maybe, nature does not like to fill space with this substance, and that stops the water from pouring out? However, some people also argued that perhaps the atmospheric pressure - the weight of the air in the atmosphere, which was known since a few years to have a measurable density - may be the culprit instead. There was a definite need for more experiments.

Torricelli-type experiments with pipes filled with mercury - the height of the mercury level is independent of the shape of the vessel, or the inclination angle (via the Institute and Museum of History of Science, Florence).

... via Florence

In Florence, Evangelista Torricelli, a student of Galileo, had the ingenious idea to replace the water in Berti's experiment by mercury - a fluid about 13 times denser than water. By this procedure, Berti's setup became much more easy to handle - what was necessary now were vessels just a tenth in size then those used by Berti. When Torricelli repeated the Berti-type experiment, he found that the column of mercury dropped to a height of about 760 millimetre - that was the origin of the instrument we now call a barometer. But what the most interesting result: the height of the mercury level in the pipe above the level in the tub does not depend of the inclination of the pipe, and it does not depend either of the apparently empty volume above the mercury level in the pipe. This was easy to see if the experiment was repeated with vessels with all kind of sizes and shapes. Now, especially this second result was very hard to arrange with any concept of the abhorrence of the vacuum - apparently, the size of this vacuum didn't play a role at all. But was it indeed the atmospheric pressure, the weight of the air around us, which stopped the mercury from completely pouring out of the pipe into the tub? It was a prime candidate, but how could one know that for sure?

and Rouen ...

News about Torricelli's experiments spread quite fast across Europe: travelling scholars told about them to their colleagues, and some scientists maintaining already regular newsletter services sent around descriptions to their interested readers. Blaise Pascal lived at the time in Rouen, some miles west of Paris, where his father worked as a tax collector for the town. Both father and son had a vivid interest in science, and they heard the news from Italy by a friend who visited them and suggested that they join forces to repeat the experiments of both Berti and Torricelli. In fact, Rouen was a well-suited place to do so, because it was the location of the best glass manufacture of France of the time, and high-quality glass jars were essential for successful experiments.

So, in early 1647, the Pascals repeated and refined Berti's experiment with big glass tubes filled with water and with red wine, as well as Torricelli's experiments with mercury. Some of the experiments were done in public, with Rouen citizens as interested witnesses. Especially the experiment with wine rose much interest - even for the science's sake, since some had argued that the empty space at the top of the tubes would be filled with the vapour of the fluid (correctly, in fact), and that this vapour would push the fluid away (not true) - thus, the level of the more volatile vine should be lower that the one of water. In the experiment, the column of wine was higher - because, as Blaise Pascal explained, the density of wine is lower than that of water, and thus a higher column of wine is required to balance the same external atmospheric pressure. Pascal, like many others, was convinced that the pressure of the air kept the fluids from pouring out of the tubes - but he still needed a way to prove this.

... to the Puy the Dôme

There is a debate among historians who had suggested first to conduct the Torricelli experiment on a mountaintop. Some argue that it was Descartes' idea, some assign priority to Pascal. Anyway, while writing up a report on the Rouen experiments and discussing their results with other scholars some time in late 1647, Pascal understood that if the weight of the air is indeed to driving force in all these experiments, it should be lower the higher the place where experiment is done, since then the layer of air above is thinner. Thus, the column of mercury in Torricelli's experiment should be the lower the higher the place where the experiment is performed. Pascal had no clue how big the effect might be, but he thought, and hoped for, that the about 1000 metre of difference in altitude between his hometown of Clermont-Ferrand and the peak of nearby Puy de Dôme might be enough. Thus, the letter to his brother-in-law, Florin Périer.

I am not sure if it took Périer some time to get warm to the idea to carry some pounds of mercury and fragile glasswork on top of Puy de Dôme just because his brother-in-law, sitting comfortably at home in Paris, had some new ideas about esoteric topics such as the weight of the air and empty space. The experiment was performed only about one year after Pascals letter - but for sure, after it was done, Périer like everyone else was excited about its outcome.

On September 19, 1648, Florin Périer and some friends perform the Torricelli experiment on top of Puy de Dôme in central France. The height of the mercury column is 85 mm less than in Clermont-Ferrand at the base of the mountain, about 1000 metre below. (From Louis Figuier, Les merveilles de la science, Vol. 1, 1867. According to this illustration, Périer and company not only climbed up the mountain, they also travelled in time, since their clothes follow the latest fashion of the 18th century.)

Finally, on Saturday, September 19, 1648, Florin Périer and some of his friends from Clermont-Ferrand embarked on the experiment. Early in the morning, they measured the height of the mercury column in two Torricelli experiments at a low-lying place in town, the Jardin des Minimes, the garden of a monastery - it was 711 mm. While one of the instruments was left behind there and observed during the day by a monk, the other was carried on top of the Puy the Dôme. To the big surprise of all, there, about 1000 metre higher than where they had started, the height of the column was only 627 mm! Florin and his friends repeated the measurement several times, and took several measurements on their way back. It was all consistent: while they climbed down the mountain again, the column of mercury climbed up in the glass tube, and back to the monastery, it was again at 711 mm, the height the stationary reference instrument had held during the whole day.

Florin Périer was so surprised and amazed by this big effect that he repeated the experiment the next day. This time, less arduously and fitting to a Sunday, he carried the instrument only the 50 metres on top of the tower of the cathedral of Clermont-Ferrand. This difference in height was enough to be clearly measurable, about 4 mm. Blaise Pascal, when hearing of the result, immediately set out to reproduce the experiment at the Tour Saint-Jacques in Paris, where a statue now pays tribute to Pascal and the experiment.

The results of the Puy de Dôme provided very strong evidence that it is indeed the weight of the air, thus the atmospheric pressure, which balances the weight of the mercury column in Torricelli's experiment. Hence, Torricelli's instrument measures this pressure - it is a barometer. And since the change in pressure with height is very well detectable, the barometer serves as an altimeter at the same time - as it is still used in aviation today.

In appreciation of the contributions of Torricelli and Pascal, two units of pressure have been named after them: one Torr, now officially out of use, is the equivalent of one "mm Hg", the pressure a mercury column with a height of one millimetre. And the derived SI unit for pressure is the Pascal, where 1 Pa is the pressure of a force of one Newton exerted on an area of one square metre.

As for the nature of the empty space above the level of the fluid in the barometer, the situation was not immediately settled after the Puy de Dôme experiment. Descartes, and later his students, insisted that it was not empty, but filled with some aether, which was just everywhere. Now we know that up to the vapour pressure, which can be minimised by reducing the temperature, it is indeed a vacuum - but the vacuum is complicatedanyway.

Isn't it funny how the "emptiness" has fascinated scientists over the centuries, and the nature of the vacuum is still today subject of vivid discussion?

that's true, it's really fascinating! But I have to add, it's a funny coincidence that while I was researching this story and preparing the post, you wrote about the Casimir effect and the Cosmological Constant. I'm not sure now anymore what exactly gave me the idea for the post, but while I was thinking about it, I read about the vacuum several times: The Zeit had a discussion about the 10-meter-limit of suction pumps, another magazine featured a 20 year old Scientific American article (in the German translation) about a modern version of Berti's experiments for the use in class.

A thing that struck me about these experiments of the 1640s is that they constituted, I believe, the first big experimental research program in what we now call "Modern Science". Many different scientist at different places in Europe contributed to this program, and within a decade or so of research, with ever more sophisticated experiments and improved equipment, the notion of the vacuum, as it is still valid in the framework of classical physics, had been established.

thanks for the nice words! I thought that the story has a few nice twists - the puzzled engineers, a clueless Galileo, experiments with long tubes filled with wine and water, the Pascal wunderkind, an errant Descartes, and finally this kind of expedition on the mountaintop - so the posting had to become a bit longer ;-)

That math and science classes are in school can often be quite boring isn't, I think, a specific US problem - unfortuntely, it's the same also in Germany. The problem is, I guess, that it needs good teachers to raise interest in science with the pupils, and that often the curricula are packed with just too much stuff which has to be done and that there is no time to do play around with experiments and the like, and there is no time to tell nice stories...

But, as I told Sabine, by some funny coincidence the November issue of the German edition of the Scientific American sugggests the use of the Berti water barometer for the use in a school project! This article by Jearl Walker in the "Amateur Scientist" column was originally published in the April 1987 issue of the Scientifc American, "Making a barometer that works with water in place of mercury."

If people didn't believe that atmospheric pressure was the explanation, then presumably they didn't believe that atmospheric pressure drops with altitude! It's just that the density of the aether up there on the mountain is different, or something......

I'm afraid I have to point out one piece of information that I believe to be incorrect. The Torr is still in use -- most high vacuum systems measure the pressure in mTorr. I don't know if that's enough though.

"The followers of Aristotle tell us that these experiments do indeed show that Nature abhors vacuum, and that it is because of it that the mercury climbs the tube. And I say them: 'Does Nature abhor the vacuum more in Paris than in the Puy de Dome?' "

About the 10m limit, I run into a personal anecdote in a small rural town one year ago. Someone gave us some old pumps, and asked to go to the local workshop to ask about them. The Master of the workshop came jointly with an apprentice, and told to my friend and me: "this is a suction pump, you can use it in non-clear water, but you can not use it to raise water higher than seven meters". And he did a pause. I answered, "yes, of course". And then a pause. And my friend, then, agreed "Of course". When we were back in the car, my friend asked me: "Why?". And I feel inclined to guess that really the intention of the master was to provoke the apprentice to ask him "why" after we were out of the workshop. I feel that both the apprentice and my friend got that the master and I were exchanging some secret masonic greeting.

thank you very much for yourappreciation and attentive reading - I have fixed the "1947", it's 1647 now.

The 1867, however, is correct, if we trust the catalogue of the Bibliothèque Nationale de France. The illustration is from a 19th century popular science book, which is actually quite interesting to read, with a lot of applied science and technology.

When I saw the figure, something looked strange to me about it, until I realized that people on real contemporary illustrations of the 1640s and 1650s (such as the first two illustrations of the post) wear quite different clothes, and that the guys on this illustration out of the 19th century popular science book followed the fashion of the French enlightenment, Voltaire, Diderot, etc, mid-18th century or so, thus 100 years later than the actual time of the experiment. Just a rough estimate - I am not a fashion geek ;-)

The Torr is still in use - most high vacuum systems measure the pressure in mTorr.

thank you very much for your remark - that allows me to explain that my focus was on the "official" when I said "now officially out of use", and I wanted to make the point that in contrast to the pascal, the torr is not a SI unit. Moreover, in Gemany, and probably in the whole European Union, usage of the Torr is officially not allowed anymore in technical devices and pressure gauges.

Of course, that's the official regulation, which doesn't hinder the usage of the torr as a convenient unit of pressure. It's the same as for the astrophyscist's erg, the Angström, or the eV, all of which are not SI units, but nevertheless still in use for historical or practical reasons.

... it's just that the density of the aether up there on the mountain is different, or something.

Well, that's more the attitude of modern-day crumpy old amateur scientist and Einstein denialists ;-)...

Descartes, for example, had no problem at all to accept the air pressure as the force balancing the weight of the column of the fluid. But that didn't stop him from being convinced that the empty space in the barometer on top of the fluid was not a vacuum, but filled with aether. Of course, he had more philosophic reasons than physical proof for this opinion, but he was convinced that there has to be "something" everywhere, which is responsible for the transmission of forces, something that can happen, in his conviction, only by direct contact. He didn't like the idea of atoms, nor that of action at a distance (no proof for these concepts either at that time), so this was not unreasonable. And it was way ahead already of the older concepts that some vague abhorrence of the void by nature does forbid the vacuum...

Hi Uncle Al,

thanks for the links - but please, do not turn this in a debate about whatever aether.

Moreover, I have to say that I strongly oppose the usage of the denomination "aether" with respect to any Lorentz-symmetry breaking field - that word is burned by way too many and too diverse connotations, and only creates confusion. After all, these fields, if they exist, are not some substance or fluid...

Yes, exactly. But still I would think that the aetherists in those days would have put up a bit of a fight. I wonder how long it took for people to accept the correct explanation, and whether there were many diehards who cooked up excuses, like the MOND diehards nowadays.

As for Descartes: I have always found his idea a bit hilarious. Yes, aether rushes into the space, and the water at the bottom pushes some aether aside, so it has to sort of loop around and connect at the top somehow....."human beings are excuse-making devices", sorry I forget who said that....

Thank you very much for a great post. Most of the science books are written in a language that is hard to capture for many students. Your article proves that history and physics can be told in simpler and interesting to read English!